Marginally Trapped Ruled Surfaces and Their Gauss Map in Minkowski Space

초록

In 1991, Chen proposed a conjecture which is the relationship between biharmonic submanifolds and harmonic submanifolds in Euclidean space and quite a few related studies have supported it. Around the same time, it was proved that Chen's conjecture does not extend to submanifolds in Minkowski space. In this paper, as part of these researches, we investigate biharmonic marginally trapped ruled surfaces in Minkowski m-space and then construct some examples about them in which Chen's conjecture does not hold.

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